n = 4;
N = 171;

Ex = [  0.5266,  16.6962,  2.7494,  2.5215, ];

y = [ ...  
          6,
          6,
         10,
         10,
          6,
         15,
         12,
         16,
         14,
         10,
          5,
          8,
         11,
         17,
          6,
         18,
         11,
         11,
         11,
         20,
         10,
         16,
         11,
         11,
          9,
          6,
          8,
         16,
          5,
         10,
         10,
         12,
          6,
         15,
         10,
         10,
          8,
         14,
         10,
         10,
         14,
         18,
         16,
          9,
         15,
         15,
          9,
          1,
          1,
          1,
         12,
         13,
          1,
         11,
          1,
         11,
         10,
          1,
         14,
         13,
         10,
         15,
          1,
          7,
          7,
         16,
          1,
         14,
         16,
         10,
          9,
          9,
         11,
         15,
         13,
          9,
          8,
         18,
         10,
         10,
          7,
          8,
         10,
          8,
          6,
          1,
         17,
         14,
          7,
          9,
         12,
         11,
          6,
         13,
         12,
         11,
          1,
         12,
          1,
         18,
         13,
          8,
         15,
          8,
         10,
          8,
          8,
         12,
          8,
         14,
          1,
          9,
          1,
          1,
         14,
         11,
         14,
         10,
          9,
          9,
          8,
         12,
         10,
         11,
         12,
         14,
         11,
         13,
         11,
         12,
         10,
          1,
         13,
         11,
         13,
         11,
          1,
         10,
         11,
         11,
         11,
          8,
         14,
         11,
          1,
         10,
          9,
          8,
          8,
         10,
         16,
         13,
         12,
         15,
         12,
          1,
         11,
         12,
         11,
          5,
         10,
         10,
          7,
          1,
          1,
          8,
          1,
          9,
         16,
          7,
          9,
];

x = [ ...  
      1,     18,      4,      4,
      1,     17,      1,      1,
      1,     15,      1,      1,
      1,     16,      3,      3,
      1,     17,      4,      4,
      0,     15,      3,      4,
      1,     15,      2,      1,
      0,     15,      2,      2,
      1,     16,      4,      4,
      1,     16,      3,      3,
      0,     17,      3,      2,
      1,     16,      2,      2,
      0,     15,      2,      2,
      0,     15,      4,      4,
      1,     15,      2,      3,
      0,     15,      4,      3,
      1,     15,      3,      4,
      0,     15,      2,      2,
      1,     16,      3,      3,
      0,     16,      4,      3,
      1,     16,      2,      1,
      1,     16,      4,      2,
      1,     16,      4,      4,
      1,     16,      1,      1,
      1,     16,      4,      3,
      1,     16,      3,      1,
      1,     15,      2,      2,
      1,     15,      3,      1,
      1,     15,      1,      1,
      0,     15,      4,      0,
      0,     17,      2,      1,
      0,     15,      2,      3,
      1,     15,      3,      2,
      0,     15,      2,      2,
      1,     15,      1,      1,
      0,     16,      2,      2,
      1,     16,      3,      3,
      0,     15,      2,      2,
      1,     15,      1,      1,
      1,     16,      2,      1,
      1,     16,      4,      4,
      0,     16,      3,      3,
      1,     16,      4,      4,
      0,     15,      2,      1,
      1,     15,      1,      2,
      0,     15,      2,      2,
      1,     19,      0,      1,
      0,     18,      2,      2,
      1,     15,      1,      1,
      1,     15,      4,      4,
      0,     16,      1,      1,
      1,     16,      1,      1,
      0,     17,      2,      1,
      1,     15,      1,      1,
      1,     15,      3,      2,
      1,     15,      1,      2,
      0,     15,      2,      1,
      0,     18,      1,      1,
      0,     16,      2,      1,
      0,     17,      1,      2,
      1,     18,      1,      1,
      0,     16,      2,      2,
      0,     17,      2,      1,
      0,     15,      3,      2,
      0,     17,      1,      1,
      1,     16,      4,      2,
      1,     16,      2,      2,
      1,     16,      4,      4,
      0,     16,      1,      0,
      0,     17,      4,      4,
      1,     16,      3,      3,
      0,     17,      4,      3,
      1,     16,      2,      2,
      0,     16,      2,      1,
      1,     16,      2,      3,
      1,     17,      1,      1,
      0,     17,      1,      2,
      1,     17,      4,      4,
      1,     17,      1,      1,
      1,     16,      1,      1,
      1,     17,      4,      3,
      0,     18,      2,      2,
      1,     17,      4,      4,
      0,     18,      3,      3,
      1,     17,      2,      1,
      1,     17,      1,      1,
      1,     16,      2,      3,
      1,     16,      4,      4,
      1,     18,      3,      1,
      0,     18,      2,      1,
      1,     17,      2,      1,
      0,     17,      2,      2,
      0,     16,      1,      1,
      0,     17,      2,      2,
      1,     16,      2,      1,
      1,     17,      2,      1,
      0,     18,      2,      2,
      0,     17,      4,      3,
      1,     18,      2,      1,
      0,     16,      2,      1,
      0,     17,      2,      3,
      0,     22,      3,      1,
      0,     16,      0,      2,
      0,     18,      3,      2,
      0,     16,      3,      3,
      0,     18,      2,      1,
      0,     16,      2,      1,
      0,     17,      2,      1,
      0,     17,      1,      1,
      0,     18,      2,      1,
      1,     17,      2,      2,
      1,     17,      3,      3,
      1,     18,      2,      2,
      1,     18,      2,      1,
      1,     18,      2,      3,
      1,     18,      1,      1,
      0,     17,      1,      2,
      1,     17,      2,      4,
      1,     18,      3,      2,
      0,     18,      4,      4,
      0,     17,      4,      1,
      1,     18,      1,      1,
      1,     18,      1,      1,
      0,     17,      1,      1,
      1,     17,      1,      1,
      0,     18,      2,      1,
      0,     18,      4,      2,
      1,     18,      2,      1,
      0,     17,      3,      3,
      1,     18,      2,      4,
      1,     19,      1,      1,
      1,     19,      1,      2,
      1,     19,      2,      1,
      0,     19,      1,      2,
      1,     19,      1,      1,
      1,     19,      2,      3,
      1,     18,      2,      1,
      1,     17,      3,      4,
      1,     18,      4,      4,
      1,     17,      2,      2,
      0,     18,      4,      4,
      0,     18,      2,      2,
      1,     17,      2,      4,
      1,     19,      2,      1,
      1,     17,      2,      2,
      1,     18,      2,      3,
      0,     18,      4,      3,
      0,     19,      1,      1,
      0,     19,      1,      1,
      0,     18,      1,      1,
      1,     18,      1,      1,
      1,     18,      1,      4,
      0,     18,      1,      1,
      1,     17,      4,      4,
      1,     17,      1,      2,
      1,     17,      1,      1,
      1,     18,      4,      4,
      0,     18,      1,      2,
      1,     17,      2,      2,
      1,     17,      1,      2,
      1,     18,      1,      1,
      1,     18,      4,      4,
      0,     18,      2,      1,
      0,     19,      1,      1,
      1,     19,      2,      3,
      1,     18,      3,      1,
      1,     18,      1,      1,
      0,     20,      2,      2,
      0,     17,      3,      1,
      0,     21,      1,      1,
      0,     19,      1,      1,
];

p_true = [ ...  
      0.096203,
      0.000000,
      0.000000,
      0.002532,
      0.017722,
      0.037975,
      0.022785,
      0.081013,
      0.070886,
      0.141772,
      0.118987,
      0.078481,
      0.078481,
      0.068354,
      0.083544,
      0.040506,
      0.015190,
      0.030380,
      0.012658,
      0.002532,
];

p_empirical = [ ...  
      0.122807,
      0.000000,
      0.000000,
      0.000000,
      0.017544,
      0.046784,
      0.035088,
      0.093567,
      0.076023,
      0.146199,
      0.134503,
      0.076023,
      0.052632,
      0.064327,
      0.046784,
      0.046784,
      0.011696,
      0.023392,
      0.000000,
      0.005848,
];
